双分数布朗运动重整化自相交局部时的光滑性

Smoothness for the Renormalized Self-Intersection Local Time of Bifractional Brownian Motion

设B^H,K={B^H,K(t),t≥0}是取值于Rd中Hurst指数为H∈(0,1)和K∈(0,1]的双分数布朗运动.它是分数布朗运动的一个推广.该文考虑了B^H,K重整化自相交局部时的光滑性问题.主要运用Malliavin分析中混沌展开的方法,在Meyer-Watanabe意义下,得到了B^H,K重整化自相交局部时是光滑的.该文结论推广了分数布朗运动的相关结果.

Let B^H,K={B^H,K(t),t≥0}be a bifractional Brownian motion in Rd with Hurst indexes H∈(0,1)and K∈(0,1].This process constitutes a natural generalization of fractional Brownian motion(which is obtained for K=1).In this paper,we research the smoothness of the renormalized self-intersection local time of B^H,K.By the chaos expansion method of Malliavin analysis,we obtain the smoothness of the renormalized self-intersection local time of B^H,K in the sense of Meyer-Watanabe.And our result generalizes that of fractional Brownian motion.